If you flip three fair coins, what is the probability that the first two flips will both be heads, and the third flip will be either heads or tails?
Answer: $\text{Probability} = \dfrac{\text{Favorable outcomes}}{\text{Total possible outcomes}}$ If you flip three coins, there are $2$ possible outcomes for each individual flip, so there are $2\times2\times2=8$ total possible outcomes. Since the coin is fair, each outcome is equally likely. Each path through the tree represents one outcome. The green paths show the $2$ favorable outcomes. $\text{H}$ $\text{T}$ $\text{First}$ $\text{H}$ $\text{T}$ $\text{H}$ $\text{T}$ $\text{Second}$ $\text{H}$ $\text{T}$ $\text{H}$ $\text{T}$ $\text{T}$ $\text{H}$ $\text{T}$ $\text{H}$ $\text{Third}$ The probability of getting heads on the first two flips, and either heads or tails on the third flip is $\dfrac28$. We can simplify this fraction to $\dfrac14$.